Mathematics: In the figure below, AABC is similar to A EFG. What is the length of EG? Enter only the number. A 5 N 3 12 16 F G B The solution is

In the figure below, AABC is similar to A EFG.

gomezjuana123

08.12.2021

EG = 20

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are in proportion , that is

$\frac{EG}{AC}$ = $\frac{EF}{AB}$ , substitute values

$\frac{EG}{5}$ = $\frac{12}{3}$ = 4 ( multiply both sides by 5 )

EG = 5 × 4 = 20

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itsnotxavier

19.01.2023

Given:

AB is the diameter of a circle whose center is the point (4,-3).

Coordinates of A are (-1,5).

To find:

The measure of AB.

Solution:

Let point O(4,-3) be the center of the circle.

Then, OA is the radius of the circle.

We know that, diameter of a circle is twice of its radius.

So, AB=2(OA) ...(i)

Distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using distance formula, the distance between O and A is

$OA=\sqrt{(-1-4)^2+(5-(-3))^2}$

$OA=\sqrt{(-5)^2+(5+3)^2}$

$OA=\sqrt{25+(8)^2}$

$OA=\sqrt{25+64}$

$OA=\sqrt{89}$

Now, using (i), we get

AB=2(OA)

$AB=2(\sqrt{89})$

$AB=2\sqrt{89}$

Therefore, the measure of AB is $2\sqrt{89}$ units.

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